The most common method for diagnosis of cardiac electrophysiological processes routinely used in clinical practice is electrocardiography (ECG) in 12 standard leads. Simplicity and low cost of a standard electrocardiographical study together with its relatively high informativity have lead to its extremely widespread use in the daily practice.
However, electrocardiographical method has principled limitations. Activity of certain myocardium compartments is inadequately reflected in electrocardiographical signals registered in standard leads. As an example, one may name difficulties in ECG-diagnosis of myocardial infarction of back-basal compartments of the left ventricle. Furthermore, according to the superposition principle in electrodynamics, any electrocardiogram is the sum of electric potentials coming from sources in a great number of myocardium points. Since electrophysiological processes in different areas of the cardiac muscle proceed simultaneously, it is rather difficult to determine a local electric activity of the myocardium on standard ECG-leads. For example, an atrial re-polarization wave in humans in conditions of a normal cardiac rhythm is not revealed in ECG, as it is “hidden” by a high-amplitude QRS-complex reflecting a ventricular depolarization. A vector-electrocardiography method is characterized by the same limitations.
Greater possibilities are provided by a method for surface electrocardiographical mapping of the chest. The method consists in a synchronic registration of multiple (from 40 to 250 and more) unipolar ECG-leads from the chest surface and in constructing maps of distribution of an electric potential over the chest surface by interpolation for each discrete moment of the cardiocycle.
However, this method does not allow one to determine more precisely a local electric activity of the myocardium. If an electrode is located on the chest surface, contributions to ECG-signal from the nearest and most remote, regarding a registration electrode, segments of the myocardium differ from each other by approximately one order. For an electrode located on the heart surface, this difference is three orders. In this connection, for revealing a local electric activity of the heart, methods of invasive ECG registration are used with an attempt to bring electrodes closely to the heart surface as much as possible.
Transesophageal electrophysiological study of the heart is based on inserting a probe with registration electrodes into the esophagus cavity. The esophagus at its certain part adjoins close enough to posterior wall of the left atrium and to posterior wall of the left ventricle; therefore, intraesophageal ECG-signals selectively register the activity of these heart compartments. Intraesophageal electrocardiography is applied, in particular, for differential diagnosis of supraventricular and ventricular arrhythmias (Transesophageal electrostimulation of the heart (under edit. Sulimov V. A., Makolkin V. I.). Moscow: Meditsina, 2001.—208 pp. [in Russian]).
However, the above-mentioned method permits one to reveal a local electric activity only of individual structures of the heart.
For a complex evaluation of cardiac electrophysiological processes and topical diagnosis of cardiac rhythm disturbances, an invasive electrophysiological study of the heart based on the direct registration of a set of electrograms from epicardial or endocardial surface of the heart is carried out. Methods indicated may be applied on “open-heart” in conditions of thoracotomy, as well as on the basis of intervention technologies of inserting registration devices (catheters) into cardiac cavities by transvascular access or into pericardial cavity by its fluoroscopically-guided transskin puncture.
Up-to-date realizations of methods afore-said are directed to a precise determination of three-dimensional (3-D) coordinates of registration electrodes by non-fluoroscopic techniques and to a visualization of results in the form of isopotential and isochronous maps on heart compartment models with means of computer graphics. Computer models of heart compartments are constructed by a great number of electrogram-registration points with known coordinates, as well as on the basis of computer (CT) or magneto-resonance (MRT) tomography data of the heart (Revishvili A. Sh., Rzaev F. G., Djetybaeva S. K. Electrophysiological diagnosis and intervention treatment of complicated forms of heart rhythm disturbances with using a system of three-dimensional electro-anatomical mapping.—Vestn. Aritmol. 2004, 34: 32-37 [in Russian]; Pokushalov E. A., Turov Shugaev P. L., Artemenko S. L. Radiofrequency ablation of ventricular tachycardia by transpericardial access.—Vestn. Aritmol. 2006, 44: 58-62 [in Russian]).
To this group of methods, one may refer methods for non-contact endocardial mapping based on inserting a “swimming” balloon catheter into cardiac cavities, registering a set of electrograms on the heart surface and reconstructing endocardial electrograms by computational way on data obtained (Schilling R. J., Kadish A. H., Peters N. S. et al. Endocardial mapping of atrial fibrillation in the human right atrium using a non-contact catheter.—European Heart Journal. 2000, 21: 550-564).
A disadvantage of above-disclosed methods that is eliminated by the present invention consists in their invasive character.
Analogues of the present invention are methods for reconstructing electrograms at internal points of the chest by computational way on data of synchronic registering a set of ECGs on the chest surface.
These methods are based on solution of the inverse problem of electrocardiography. Statement of the inverse problem of electrocardiography (IP ECG) is formulated in works of Barr D., Spach M Solutions of the inverse problem directly expressed in terms of potentials//Theoretical fundamentals of electrocardiology [Russian translation under edit. Nelson K. V. and Geselovitz D. V.]—Moscow: Meditsina 1979, pp. 341-352; MacLeod R. S., Brooks D. H. Recent progress in the inverse problem in electrocardiology//IEEE Eng. in Med. Bio. Mag. 17:1, pp. 78-83, January 1998; Rudy Y., Messinger-Rapport B. J. The inverse problem in electrocardiography: Solutions in terms of epicardial potentials. CRC Crit. Rev. Biomed. Eng. 1988, 16: 216-268.
From the mathematical standpoint, IP ECG is a problem of harmonic continuation (propagation) of the potential in the direction of sources, i.e., the Cauchy problem for the Laplace equation. Computational domain, in which the Laplace equation is given, represents a part of the chest bounded by heart's external surface, chest surface on which ECG-registration is accessible, and by imaginary cross-sections of the chest at the level of the diaphragm and clavicles.
At the part of the chest surface where ECG-registration is accessible values of the electric potential obtained as a result of ECG-mapping as well as the condition of equality-to-zero of a potential normal derivative are given. These data compose Cauchy conditions.
The Cauchy problem consists in finding the electric field potential in domain indicated and its trace on the heart surface and on cross-sections of the chest in such a way that the potential in computational domain would satisfy the Laplace equation, while on the torso surface where ECG-registration is accessible it would satisfy the Cauchy conditions.
According to Hadamard, the Cauchy problem for the Laplace equation is ill-posed, as any negligible errors in the condition may result in arbitrary large errors in the solution. When solving the Cauchy problem for the Laplace equation, it is necessary to apply special so-called regularizing algorithms (Denisov A. M. Introduction to the theory of inverse problems [in Russian].—Moscow: Moscow State University, 1994; Tikhonov A. N, Arsenin V. Ya. Methods for solution of incorrect problems [in Russian].—Moscow: Nauka, 1986, 312 pp.).
To solve the Cauchy problem for the Laplace equation in an above-disclosed statement (the inverse problem of electrocardiography) by an analytical way appears to be impossible. Therefore, the inverse problem of electrocardiography is numerically solved by means of computational mathematics with using computer techniques.
One of the ways for solving the inverse problem of electrocardiography is a method for reconstructing the electric field on “quasi-epicard”, i.e., on a conditional spherical surface surrounding the heart. From the mathematical standpoint, this method is based on representation of the heart electric field potential in the form of a harmonic polynomial (sphere function), whose coefficients are found from the condition of equality (or the minimum of mean square deviation) of polynomial values and values of an ECG-signal at points of its registration with taking into account the equality-to-zero of a potential normal derivative on the chest surface. For providing the stability of solution, a polynomial of degree not higher than 4 is used. An essential disadvantage of this method is that, when the radius of sphere diminishes, i.e., as “quasi-epicard” surface approximates to a real surface of the heart, the accuracy of potential reconstructing sharply drops. When “quasi-epicard” surface approximates to the chest surface, the resolution of the method in terms of revealing a local electric activity of the myocardium decreases (Titomir L. I., Kneppo P. Mathematical modeling of heart's bioelectric generator.—Moscow: Nauka, Physmathlit, 1999.—448 pp. [in Russian]; Titomir Trunov V. G., Aidu E. A. I. Noninvasive electrocardiography.—Moscow: Nauka, 2003.—198 pp. [in Russian]).
For solving boundary problems for the Laplace equation, methods of integral equations of the potential theory, more known in English-written literature as boundary element methods, are widely used (Brebbia C., Telles J., Wrobel L. Boundary element methods [Russian translation].—Moscow, Mir, 1987). The present approach to IP ECG solution is proposed in works of Taccardi E., Plonzi R., Barr R. (Barr R., Spach M. Inverse problem solutions directly expressed in terms of a potential//Theoretical fundamentals of electrocardiography [Russian translation under edit. Nelson C. V. and Geselovitz D. V.]—Moscow: Meditsina, 1979; pp. 341-352). Above-mentioned methods suppose, in particular, the representation of the heart and torso surfaces as polygonal ones, i.e., splitting boundary surfaces into a great number of triangular elements. According to the boundary element method, IP ECG for a homogeneous model of the chest is reduced to solving a system of two Fredholm integral equations of 1st and 2nd kinds, which is approximately substituted by a system of matrix-vector equations:A11x+A12y=c1,A21x+A22y=c2  (1)where Ai,j are known matrices, x1, x2 are unknown vectors having a sense of sought-for values of the potential and its normal derivatives in nodes of triangulation grids approximating the heart surface and torso cross-section surfaces, c1, c2 are known vectors calculated on known data of the problem.
In the method for noninvasive epicardial mapping suggested by Shakin V. V. et al. the following algorithm of IP ECG solution was used.
The system of matrix-vector equations (1) by means of elementary transformations was reduced to a system of linear algebraic equations (SLAE) to be resolved in explicit form:ΦH=ZHB·ΦB,  (2)where ΦH is an unknown vector having a sense of sought-for values of the potential and its normal derivatives in nodes of triangulation grids approximating the heart surface and torso cross-section surfaces, ZHB is a known matrix, ΦB is a known vector. For calculating matrix ZHB, it is necessary to use an inversion procedure of matrices entering the system (1), one of matrices to be inversed being non-square and bad-conditioned. For implementation of this procedure, constructing a Moore-Penrose pseudo-inverse matrix on the basis of SVD-decomposition of an initial matrix and substituting small singular values by zeroes were performed.
The heart and torso surfaces were represented as simplified models in the form of cylindrical and ellipsoidal surfaces to be constructed on the basis of two-projection roentgenography of the chest. Results of mapping in the form of isopotential and isochronous maps were imposed on model scanned-schemes of heart compartments. This methodology was used for revealing a localization of additional pathways (APW) at manifested WPW syndrome and ectopic sources at ventricular extrasystole (Shakin V. V. Computational electrocardiography [in Russian].—Moscow: Nauka, 1980).
In his works, Shakin V. V. has emphasized a promising outlook of the application of computer-tomography techniques for more precise constructing the torso and heart surfaces; however, this approach could not be used because of unsatisfactory development of methods for computer tomography of the heart.
The most similar to a method claimed here (prototype) is the methodology of noninvasive electrocardio graphical imaging (ECGI).
In this methodology, a surface mapping is realized with using 224 unipolar electrodes placed in a special vest to be put on a patient for a study period. The torso and heart surfaces is determined based on computer (CT) or magneto-resonance (MRT) tomography of the chest. A reconstruction algorithm is based on solution of the inverse problem of electrocardiography by the boundary element method.
The torso and heart surfaces is approximately represented as polygonal surfaces. For solving IP ECG, the system of matrix-vector equations (1) is also used, which by elementary transformations is reduced to a system of linear algebraic equationsAx=c  (3)where x is an unknown vector having a sense of sought-for values of the potential in nodes of triangulation grids approximating the heart surface and torso cross-section surfaces, A is a known matrix, c is a known vector.
The system of linear algebraic equations (3) is bad-conditioned. For its solving the Tikhonov regularization method and the iteration regularization method on the basis of GMRes-algorithm are used. The Tikhonov method is based on solving the following system instead of the system (3)(AT·A+αE)x=ATc where AT is a matrix transponated in respect to matrix A, E is an unit matrix, α is a regularization parameter (a small positive real number).
The iteration regularization method is based on solution of the system (3) by a method of sequential approximations with limiting a number of iterations on the basis of GMRes-algorithm, which belongs to a group of Krylov subspace methods (Ramanathan C., Ghanem R. N., Jia P., Ryu K, Rudy Y Electrocardiographic Imaging (ECGI): A Noninvasive Imaging Modality for Cardiac Electrophysiology and Arrhythmia//Nature Medicine, 2004; 10: 422-428; Rudy Y., Ramanathan, C., R. N. Ghanem, R. N., Jia P. System and Method For Noninvasive Electrocardiographic Imaging (ECGI) Using Generalized Minimum Residual (GMRes)//U.S. Pat. No. 7,016,719 B2, 2006).
The similar technique was used in works of Berger T., Fisher G., Pfeifer B. et al. Single-Beat Noninvasive Imaging of Cardiac Electrophysiology of Ventricular Pre-Excitation//J. Am. Coll. Cardiol., 2006; 48: 2045-2052.
This technique was applied for revealing an APW-localization at manifested WPW syndrome, ectopic sources at ventricular extrasystole and tachycardia, reconstruction of an activation dynamics of the myocardium at atrium flutter.
The essential disadvantage of the method under consideration is using a model of the chest with a constant (invariable) coefficient of specific electroconductivity. Specific electroconductivity of different organs and tissues of the chest shows essential distinctions. A variable electroconductivity coefficient of biological tissues strongly enough influences on the heart electric field in the chest what is confirmed by data of experimental research (Rudy Y., Wood R., Plonsey R., Liebman J. The effect of high lung conductivity on electrographic potentials. Results from human subjects undergoing bronchopulmonary lavage//Circulation 1982, 65: 440-445). The greatest role plays the difference in electroconductivity between lungs and surrounding them soft tissues (at 4-5 times). Potentials of the heart electric field of model sources calculated for homogeneous and inhomogeneous models of the chest differ from each other by 15%-20% (Titomir L. I., Kneppo P. Mathematical modeling of heart's bioelectric generator.—Moscow: Nauka, Physmathlit, 1999.—448 pp. [in Russian]. Thus, neglect of an electrical inhomogeneity of chest tissues may lead to greater errors of reconstructing the heart electric field.
The present invention is aimed at improving the accuracy of noninvasive electrophysiological study of the heart at the expense of taking into account a different electroconductivity coefficient of chest tissues.